Question

A series of equal quarterly payments of $25,000 for 10 years is equivalent to what future worth amount at an interest rate of 8.4% compounded at the given intervals?

(a) Quarterly

(b) Monthly

(c) Continuously

Answer 1

a.

i = 8.4% / 4 = 2.1% per quarter

t = 10 * 4 = 40 quarters

Future worth = 25000 * (F/A,2.1%,40)

= 25000 * ((1 + 0.021)^40-1)/0.021

= 25000 * ((1.021)^40-1)/0.021

= 25000 * 61.728838

= 1543220.95 ~ 1543221

b.

i = 8.4% / 12 = 0.7% per month

Effective interest rate per quarter = (1+0.007)^3 -1 = 0.0211473

t = 10 * 4 = 40 quarters

Future worth = 25000 * (F/A,2.11473%,40)

= 25000 * ((1 + 0.0211473)^40-1)/0.0211473

= 25000 * ((1.0211473)^40-1)/0.0211473

= 25000 * 61.92726687

= 1548181.67 ~ 1548182

c.

i = 8.4% / 4 = 2.1% per quarter

Effective interest rate per quarter = e^0.021 -1 = 0.02122205

t = 10 * 4 = 40 quarters

Future worth = 25000 * (F/A,2.122205%,40)

= 25000 * ((1 + 0.02122205)^40-1)/0.02122205

= 25000 * ((1.02122205)^40-1)/0.02122205

= 25000 * 62.02825967

= 1550706.49 ~ 1550706